Vibrating strain gauges



sept. 4, 1962 FledAug. l0, 1959 FIG. 1

In N

O. H. CRITCHLEY ETAL VIBRATING STRAIN GAUGES 3 Sheets-Sheet 1 Sept. 4,1962 o. H. cRlTcHLEY ETAL 3.052.116

VIBRATING STRAIN GAUGES MLV Sept. 4, 1962 O. H. CRITCHLEY ETAL VIBRATINGSTRAIN GAUGES 5 Sheets-Sheet 3 Filed Aug. 10, 1959 ZWi/Eh fr;

ot/Zy/'MS Hun/- am' /I/EWWGI/y Barron United States Patent 3,052,116VIBRATING STRAIN GAUGES Octavius Hunt Critchley, Hounslow, KennethBarron, New Southgate, London, and William Harold Kellet, Whitton,Twickenham, England, assignors to Coal Industry (Patents) Limited,London, England, a company of Great Britain Filed Aug. 10, 1959, Ser.No. 832,698 Claims priority, application Great Britain Ang. 25, 1958 2Claims. (Cl. 73-88.5)

This invention relates to vibrating wire strain gauges for embedment instructures fabricated from concret-e or similar plastic material lwhichsets hard after moulding, and particularly, although not exclusively, tosuch gauges where `a useful life of up to two decades or more may berequired. Gauges of this type are used to measure changes in strain dueto variations in the loading to which the structure is subjected yandother dimensional changes that may occur upon ageing of the material ofthe structure.

It is well known .that the natural frequency of vibration of `a wireheld in tension between two supporting end clamps, varies rapidly as thespacing between these supports is changed. This property may be used forthe measurement of strain -by attaching the supporting end clampsdirectly to the structure in which it is wished to study the strainvariations and the property may be expressed functionally by anexpression derived from Mersennes and Hooks laws. If the structure 4isfashioned from a plastic material, such as concrete, that sets hardaiter moulding, the wire and its `supports may be embedded in thestructure. To measure the strain variations, it is necessary only ttoset the wire vibrating and to determine the resulting .changes in thenatural frequency of vibration of Ithe wire. This may be done bymounting close to the wire a small U-shaped permanent magnet assemblyupon the limbs of which are wound coils of insulated copper wire. If anelectric current .pulse is passed through the coil the strength of thepolar-ising magnet lield is yaltered yand :the ten-sinned strainmeasuring wire, which is part ofthe magnetic circuit, experiences aforce normal to its axis and is set into vibration. These vibrationsalter the reluctance of the magnetic circuit and so change the fluxlinking :the coil, with the result that an alternating is generatedhaving a frequency which is equal to the natural frequency of Ithe wire.

The application of vibrating wire strain gauges to the problem ofdetermining strain in a structure fabricated from concrete or :similarplastic material which sets hard after moulding, has already beenproposed. In such application, -the gauge is embedded in the structureand comprises a wire held by end clamps attached to ilat plates or discsarranged rwith their planes normal to the axis of the wire. These endplates are held firmly by the structural material in which they areembedded and transmit movements in the material to the end clamps withnegligible loss. Protection against damage is afforded to the wire ofthe gauge by =a Itube which smrounds the ywire and which is ixed to theend plates. It has heretofore been assumed that it is necessary toensure that the tube does not inhibit the movement between the endplates and it has previously been proposed to make this tube telescopicor to form the tube of some material which is much lweaker .than thematerial of the structure in which it is set.

However, the known gauges suffer from the disadvantages that they do noteffectively and persistently exclude moisture from the wire over .thelong period of time for which the strain gauge is expected to remain inaccurate use, particularly when the `strain gauge is to be embedded inIdamp or wet structures, `and that it is not possible to ICC :adjust theinitial :or zero frequency of the string immediately prior to itsembedment in the structure. A further serious disadvantage is thedelicacy of construction of the previously proposed types `of gaugeswhich makes them inconvenient to handle, particularly in iieldconditions. The `telescopic tube type tof gauges also Ifails because itis not possible eectively to seal the joint between lthe tube parts,`and the `other -type above mentioned often fails because lthe materialof which the tube is made is not durable. After the gauge has been madeup and is ready for use, there 'has 'also previously been no mea-.nsprovided for the adjustment of the natural frequency :of the wire to thedesired initial reference or zero level of frequency.

The present invention provides a vibrating wire strain gauge forembedding in a :structure fabricated from concrete or similar materialcapable of setting hard, comprising -a metal tube which extends betweena pair of anges and encloses a wire of ferro-magnetic material sealed inthe gauge, and an electro-magnet adjacent the wire, in which the gaugeis constructed in accordance with .the formula:

wirwar-1)] where r, t, and i; have the values assigned to them in the@foregoing description.

The matching of the composite elastic modulus of the whole gauge to thatof the material is achieved by a judicious choice `of the ratio of thewall thickness of .the tube to the diameter of the tube, of the radiusof end discs incorporated in the gauge, and of the elastic modulus ofthe material Iof which the tube is formed. The manner of calculation ofthe desired design parameters of the gauge are hereinafter described.

According to sa further feature of the invention, means are provided bywhich the tension of the wire can be adjusted so that fthe initial yorzero reference frequency of the wire can be adjusted immediately priorto its embedment in the structural material. This is achieved bydesigning `one of the end clamps to include la Vernier screw which may:advantageously be covered by a protective cap Ito keep out moisture. l

By Way of example, the invention wi-ll be hereinafter described withreference to the accompanying drawings in which,

FIGURE 1 is a plan view partly in section of one form of gaugeconstructed according to the present invention,

FIGURE 2 is a longitudinal cross-sectional View of the gauge of FIGURE1,

FIGURE 3 shows two gauges embedded in a block prior to nal embedment ina structure, and

FIGURE 4 shows -an alternative form of gauge.

As shown in FIGURES 1 and 2 of the accompanying drawing, the vibratingwire strain gauge comprises a brass protective tube 1 of 0;25 inchdiameter and a wall thickness of 22 S'.W.G., the tube 1 extendingbetween end members 2 and 3 and a wire W which is a high grade musicalstring of silver plated steel 0.010 inch in diameter, and which extendsaxially through the tube 1 between the end members 2 and 3.

The end member 2 is formed by a hub portion 4 and an integral flange 5two inches in diameter. Through the hub 5 extends a non-axial bore 6 inwhich is situated 4a clamping block 7 between which and the wall of thebore 6 is clamped one end Wa of `the Wire W, the block 7 being held inclamping position by screws 8. rllhe outer end of the bore 6 is closedby a plug 9 to prevent ingress of moisture and dirt into the tube 1. l

The end member 3 is also formed by hub portion '10 provided with anon-axial bore 11 extending therethrough and an integral iiange 12 alsotwo inches in diameter. Axially slidable within the bore 11 is aclamping element 13 having axially extending therethrough a bore 14. Theother end Wb of the wire W is clamped Within the bore 14, similar to themanner in which the end Wa is clamped VWithin the bore `6i, by means ofa clamping block 15 and Ascrews l16 which slide with the element 13 inan axially extending slot -17 in the hub 10. The outer end of theelement 13 is provided with -an internal screw thread 18 `and anexternal screw thread 19. Meshing with the Athread 19 is a nut 20 whichbears against the outer end of the hub and by which the axial positionof the element 13 relative to the hub 10 can be adjusted to set thetension in the wire W. The nut 20 which is provided with a transverseslot 21 on its outer face to facilitate rotation of the nut, can belocked in the desired position after adjustment of the tension in theWire W by means of a screw 22 which passes through a bridge 23 bearingagainst the outer face of nut 20, and which meshes with vthe thread 18in the element 13.

The outer end of hub 10, the nut 20, the bridge 23 and the screw 22 aresurrounded by a shell 24 the inner end of which is welded to the outerface of flange 12 and the outer end of which is closed by a screw cap25, the shell 24 serving to prevent 4the ingress of moisture and dirtinto' the tube 1.

Midway along the length of the -tube 1 is located -an exciter unit 26comprising la U-shaped permanent magnet 2 7 of which each of the polepieces is surrounded by coil 28 of 150 ohms resistance. The free end ofeach of the pole pieces is located adjacent the wire W. The magnet `27and coils 28 are housed in a brass box 29 welded to the tube 1, the box29 being provided with a set screw cap 30 and ran outlet 31 throughwhich can be passed the leads to the coils 28. The cap 301 is providedwith a transverse groove 32 by which the cap 30 can be tightened andreleased. The magnet 27 and coils 28 are embedded in a mass 33 ofsuitable resin.

All exposed parts of the gauges are nickel plated to inhibit corrosion.

The active length of the Wire W is 5.25 inches. The gauge may be useddirectly in the material of a lstructure, but for rougher use, such asit may experience on a constructional site, it may be desirable toprecast the gauge in a block of this material. For this purpose, -thegauge is assembled and placed in a small mould. The cap on the end ofshell 24 is replaced by -a longer blanking off rod which is screwed intothe end of shell 24 `and projects from the mould. After the material hasset and the block has been removed from the mould,

the rod is unscrewed from the shell 24. By this artifice,

an access hole is left in the block to provide 4access to the nut 20 forthe purpose 'of adjusting the tension of the wire W.

FIGURE 3 shows one form of block in which is moulded a pair of gaugeseach constructed yas above described. The block comprises two mainportions 41 and 42 in each of which is embedded -a 'strain `gauge 43 andvwhich `are interconnected main portions by a pair of web 'portions 44and 45. Through the web portion 44 extends Vto have end flanges whichare of suicient diameter to begripped well by the concrete or other massof structural material, but they must not be so large as to produce anappreciable local change in the nature of the material. Again, thediameter of the tube protecting the Wire must be adequate to meet thecriteria for matching of elastic moduli set out below but it must alsohave suflicient length so Aas to meet the requirement that the tion ispossible.

length of the gauge be large compared to its` diameter. On the otherhand, it is desirable that the frequency of vibration of the gauge liein the region of high aural sensitivity as this has several importantadvantages, and this puts a limit on the overall length of the gauge, asthe natural frequency of vibration falls inversely with `the length ofthe string. Because the Well known techniques for the transmission,amplification and measurement of audio frequencies have been influencedby the arts of speech transmission in communications engineering and forwhich reason avail-able equipment Works well in the frequency band of500 c./s. to 3,000 c./s., a gauge frequency in this range is desirablefor eicient plucking and good -output from a reasonably small magneticsystem. Such output frequencies may be readily handled by simpleelectronic apparatus and sok that it may be readily heard if it is`desired to use aural methods for frequency determination.

Using an unloaded string, which has a frequency of vibrating lying inthe range of 400 to 1200 cycles per second, the most `convenientdimensions for the gauge are as stated above with respect to thelapparatus shown in FIGURES 1 and 2.

It is further necessary, according to the present invention, to obtain amatch between the effective elastic modulus of the gauge assembly andthat of the structural material. This may involve a relation betweenthese moduli and the diameter of the end flanges, the overall diameterof the protecting tube and its wall thickness -as well as the materialfrom which the tube is spun or drawn. Considering the general case, andreferring to FIGURE l,

Let E=the effective modulus of elasticity of the combination of thegauge and the structural material in which it is to be embedded,

Ec=the modulus of elasticity `of sai-d structural material,

Em=the modulus of elasticity of the material from which the protectingtube has been fashioned,

Em=the effective modulus of elasticity of theprotecting tube as a whole,

A1: the total cross-sectional area of the end flanges,

R=the radius of the end anges,

A2=the overall cross-sectional area of the protecting tube,

r=the external radius of the protecting tube,

t=the wall thickness of fthe protecting tube and A3=the residualcross-sectional area from the outside of the protecting tube to the rimof an end iiange.

Now, for ideal matching the eiective modulus of elasticity of thematerial between the `gauge flanges (i.e. concrete-j-metal tube) shouldhave the same modulus of elasticity as concrete.

Ignoring the etect of the string,

@driver-Dl (III) From Equation (III) a number of important inferencesmay be drawn, namely: (a) -If Em Ec that is if the -structural materialis stronger than the protecting tube, then i is fractional and no solu-This means that it is impossible to match whence the elastic moduli ifthe tube is made of material having an elastic modulus less than theconcrete.

(b) If Em Ec which will be the case with a protecting tube of steel,brass or some like alloy, then l and the only realisable solutions willbe for The conditions for an exact match may be calculated directly from(IV). (c) Although R, the radius of an end flange does not appear inEquation (IV) and it would seem that this dimension has no significanceas a design parameter, this is only true for conditions of an exactmatch ofthe elastic moduli. It is unlikely that an exact match will beobtainable because material of the precisely specified dimensions maynot be available. Hence, the diameter of the flanges has signicance asmay be seen from Equation (111). The matter will be treated in moredetail later, but in general the llanges should be yas large ascompatible with other design considerations.

Given the wall thickness of the brass tube l, it is now possible tocalculate the diameter of this tubing necessary to obtain a perfectmatch of the elastic moduli.

Let it be assumed that the wall thickness is 22 S.W.G.

Take the elastic modulus of concrete, the structural material to be usedEc=4 106 p.s.i. and that of brass Then, substituting in (IV), we have avalue for r of 0.175 inch. Hence, for perfect matching of t-he elasticmoduli a brass tube of Wall thickness 22 S.W.G. and of 0.35 inchdiameter is required. However, it may not be possible to either obtainor use a tube of the prescribed size and, hence, it is necessary toexamine the error introduced into the match if a tube of dilerent sizeis used.

Assume, for instance, that a tube of 0.25 inch diameter only isavailable.

Consider again Equation (II) which may be re-writtenE,=t(2r-t)Em;-2(RZ12)E (V) where E' is the elfective modulus under thenew conditions.

Then, in the case in point,

E=4.03 X106 p.s..i.

The difference between this effective value and the modulus for concreteof 4 1l06 p.s.i. is negligible. However, examination of Equation (V)does yindicate that it is desirable in .this case for the radius of theend flanges to be |as large as convenient, if it is not possible to meetthe conditions for accurate matching. As the modulus of concrete issomewhat different in compression and tension, this is an importantdesign consideration.

An error will be introduced into the embodiment of FIGURES l and 2 byvirtue of the arran-gement of the exciter unit 26 but in most instancesthis error will be of negligible proportions. However, apparatus can beconstructed which eliminates even this error, by elimination of theexciter unit box, and one form of such apparatus will now be `describedwith reference to FIGURE 4.

The embodiment of FIGURE 4 differs from that of FIGURES 1 and 2 only inthe arrangement of the tube 1 and the exciter unit 26. In thisembodiment the unit 26 is enclosed in the tube f1, the tube 1 beingprovided with an outlet 51 to which can be connected a conduit 52 forthe passage into the tube l of the leads 53 to the coils 28 of the unit26.

One example of the apparatus shown in FIGURE 3 and constructed inaccordance with the present invention has the following specifications.

If tube 1 is constructed of 20 S.W.G. mild steel tube and has a wallthickness of 0.036 inch, the elastic modulus of mild steel, Em, i-staken as 30 106 psi., and that of concrete Ec is taken as 4 10G p.s.i.,then 5:7.5 and the radius, r, -to the outside of the tube may becalculated from equation (IV). This gives a tube radius of 0.522 inch oran outside diameter of 1.044 inch. The nearest stock size is 1%6 inchwhich .is 1.063 inch. The discrepancy is only 0.019 inch, less than 2%.For end anges of 2.00 inches diameter, the effective elastic modulusofthe embedded gauge is 3.98 10fi p.s.i. which does not represent asignificant error.

In either of the above described embodiments the vibrating wire straingauge may be pressurised to give added protection against ingress ofmoisture. In the embodiment of FIGURE 4, the conduit 52 may be used forpressurising the gauge. Under extremely wet conditions the conduit 52may be of sufficient length to be accessible at the external surface ofthe structunal material in which it is embedded and a pressure gauge maybe attached to the end of the conduit -to allow frequent checking of thepressure.

In the embodiment of FIGURE 4, two exciter uni-ts for exciting the wireinto Vibration may be used. With two exciter units placed at the quarterpoints of the wire, it is possible to obtain continuously sustainedinstead of plucked oper-ation.

The manner of operation of either of the above described vibrating wirestrain gauges is lthe same as that for lthe known instruments.

The wire frequency is measured either by comparison with another wire ofvariable frequency which is in continuously sustained oscillation, bycomparison with an accurately calibrated variable frequency oscillator,or it is counted and timed yby decade counting units.

The wire may be plucked by a direct current, or it may be excitedsympathetically by pulsed `alternating current derived from an A.C.measuring source. When the frequency of the alternating current excitingpulse is equal to that of the wire, the amplitude of the induced vibra#tion in the wire is at a maximum. The frequency of the wire is measuredas previously during lthe decay period af-ter the exciting current haslbeen cut off.

It two magnetic exciter units are provided, one of the units isconnected to the input terminals of `au A.C. amplilier and the otherexciter unit is connected to the amplifier output. In rthis case, withthe connections in the right sense Iand the gain of the ampliersuflicient to make the loop gain equal to unity, and if the phase delayin the circuit is small and constant, then the wire will be maintainedin sustained oscillation at its natural frequency. 'Ihe frequency of`the continuously sustained oscillations of the vibrating wire of thegauge may then be determined by any convenient yfrequency measuringtechnique.

It is desirable that the gauge be independent of temperature variations.This may be almost perfectly achieved in lboth the embodiments of theinvention in which, in the form illustrated, the residual temperatureco-eliicient is very smrall.

Consider the performance with the given temperature co-efiicients forthe case of the gauge of brass or steel construction embedded inconcrete.

The respective temperature co-elicients of linear expansion are:

Concrete 6 X 106 per degree Fahrenheit (approx.) ac Steel 6.8 106 perdegree Fahrenheit (approx.) as Brass 10.4 l06 per degree Fahrenheit(approx.) aB

The error introduced by temperature change will be due to differentiallinear expansion between 4the parts of the gauge. If all the temperatureco-elcients are the same, there is no error.

There are three parts involved, namely, the vibrating wire, the tube andthe concrete matrix cylinder delined by the end flanges.

Let the temperature rise by p", then the steel wire Will expand by pas,land there would be la drop in the frequency of the vibration of thewire, if this movement was considered on its own.

However, the concrete between the end plates expands by pac which isless than qms. This tends to pull the Wire tight, but fails to do so by(as-ac) .and if thetube 1 did not exist there would .be a consequentreduction in frequency of 61. Nevertheless the protection tube cannot beignored `and as this in both cases (aB as aC) expands more rapidly thanthe concretercylinder dened by the end plates, compensation or reductionof the temperature co-eicient is possible.

In the case of the iirst embodiment of the invention, the Wire isenclosed in a brass tube. Now this has a temperature' coecient of linearexpansion aB which is almost double that of concrete ac. The actualdilerential change of wire tension will be deter-mined by the effectivetemperature co-e'icient of linear expansion of the composite cylinder ofconcrete and brass. The concrete restrains the movement of the brass,but has a co-etlicient less than that of the fwire. By judicious choiceof the size of the brass tube and by permitting some mismatch in thetemperature co-eicients, it is possible -to compensate completely forthe diierence between the temperature co-eficients of linear expansionin the case of this particular embodiment of the invention as depictedin FIGURE 2. Put analytically, this may be expressed as In the case ofthe second embodiment of the invention, it is not possible with steel toobtain complete compensation unless the temperature co-e'cient of linearexpanf sion of the tube is slightly higher than that of the wire. `(Thisis possible by correct choice of the steels.) Nevertheless, even if asis the same for both tube and wire, the differential co-eicient will bereduced considerably, as the larger temperature co-ecient of the tubewill force the concrete to move more than it would if the protectingtube were not present.

Expressed analytically:

Experimental work has verified that with a gauge constructed as shown inFIGURES 1 and 2, the residual temperature co-eicient of linearexpansion, when it is set in concrete, is 0.l7 106 per degreeFahrenheit, which is half an order less than would be expected byconsidering the wire and concrete alone.

We claim:

1. A vibrating wire strain gauge for embedding in a structure fabricated`from concrete or a similar material capable of setting bard, comprisinga pair of anges, a protective me-tal tube rigidly xed to said iiangesand extending between said flanges, a strain-sensitive elementconstituted by a wire `of ferro-magnetic material enclosed in said tubeand sealed in said gauge, said wire being ixed relative to said angesand being tensioned therebetween, and an electro-magnet adjacent saidWire, the dimensions of Ithe tube being chosen in accordance with theformula r=tlt+\/s t1 Where r'is the external radius of the tube, t isthe wall thickness of the tube,

E'M be; EM is the modulus of elasticity of the material of the tube, andEC is the modulus of elasticity of the structural material.

2. A vibrating wire strain gauge for embedding in a structure fabricatedfrom concrete or similar material as claimed in claim l comprisingadjusting means by which the tension of the Wire can be adjusted fromexternally of the gauge.

References Cited in the file of this patent UNITED STATES PATENTS1,708,333 Smith Apr. 9, 1929 2,148,013 Carlson Feb. 21, 1939 FOREIGNPATENTS 1,069,588 France July 9, 1954 mi.; -W

